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kupik [55]
3 years ago
10

An experiment that was carried out to study how flow rate through a solenoid valve in an automobile's pollution-control system d

epended on three factors: armature lengths, spring load, and bobbin depth. Four different levels (low, moderate, high, and extreme) of each factor were chosen, and a single observation on flow was made for each combination of levels.
Requried:
a. The resulting data set consisted of how many observations?
b. Is this an enumerative or analytic study? Explain your reasoning.
Mathematics
1 answer:
xenn [34]3 years ago
7 0

Answer:

a. There are 12 observations from the resulting data set.

b. This is an analytic study.  It compares the flow rates through a solenoid valve based on three factors at four different levels.

Step-by-step explanation:

Observations of the dependence of flow rate

Factors              Armature    Spring    Bobbin

                           Lengths      Load      Depth

Levels

Low                          1                1               1

Moderate                 1                1               1

High                         1                1               1

Extreme                   1                1               1

Total observations  4               4              4

Number of observations = 12

b) Whereas enumerative studies are statistical studies carried out to draw a conclusion on a process or a condition, analytic studies are statistical studies that compare two or more groups or sets of data to improve future performance.  The focus of an analytic study is on the process rather than the condition.  Enumerative studies tend to explain, evaluate, and describe the condition of the dataset.

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Solution:

Given value \log _{3} a=-0.631.

To evaluate the expression \log _{3} \frac{a}{3}.

Using logarithmic rule: \log _{b}\left(\frac{M}{N}\right)=\log _{b}(M)-\log _{b}(N)

$\log _{3} \frac{a}{3}=\log _{3}(a)-\log _{3}(3)

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A farmer has 300 ft of fence to enclose 2 adjacent rectangular pens bordering his barn. Find the maximum area he can close.
Margarita [4]

Answer:

Width of 37.5 feet and length of 50 feet will maximize the area.

Step-by-step explanation:

Let w represent width and l represent length of the pen.

We have been given that a farmer has 300 ft of fence to enclose 2 adjacent rectangular pens bordering his barn. We are asked to find the dimensions that will maximize the area.

We can see from the attachment that the perimeter of the pens would be 4w+3l.

We can set our given information in an equation 4w+3l=300.

The area of the two pens would be A=2l\cdot w.

From perimeter equation, we will get:

w=\frac{300-3l}{4}

Substituting this value in area equation, we will get:

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Bring out the constant:

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A=\frac{1}{4}*(600-12l)

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Now, we will set our derivative equal to 0 as:

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w=\frac{300-3(50)}{4}

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